%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU078+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:23:46 PM UTC 2026
% Result : Theorem 0.62s 0.65s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of formulae : 105 ( 28 unt; 0 def)
% Number of atoms : 352 ( 79 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 415 ( 168 ~; 179 |; 41 &)
% ( 13 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 3 con; 0-3 aty)
% Number of variables : 186 ( 14 sgn 94 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rc1_subset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( ~ empty(X2)
& element(X2,powerset(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(fc2_subset_1,axiom,
! [X1] : ~ empty(singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(t56_zfmisc_1,axiom,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_zfmisc_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( empty(X2)
& element(X2,powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(t39_zfmisc_1,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = singleton(X2)
| X1 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(t159_funct_1,conjecture,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ( one_to_one(X1)
<=> ! [X2] :
? [X3] : subset(relation_inverse_image(X1,singleton(X2)),singleton(X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t159_funct_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t144_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ! [X2] :
~ ( ! [X3] : relation_inverse_image(X1,singleton(X2)) != singleton(X3)
& in(X2,relation_rng(X1)) )
<=> one_to_one(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_funct_1) ).
fof(t173_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> ( relation_inverse_image(X2,X1) = empty_set
<=> disjoint(relation_rng(X2),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t173_relat_1) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( empty(X3)
& element(X2,powerset(X3))
& in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(d13_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(apply(X1,X4),X2)
& in(X4,relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
fof(d5_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X1,X4)
& in(X4,relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(t2_xboole_1,axiom,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( in(X1,X2)
| empty(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(c_0_20,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( ~ empty(X2)
& element(X2,powerset(X1)) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(c_0_21,plain,
! [X77,X78] :
( ( element(X77,powerset(X78))
| ~ subset(X77,X78) )
& ( subset(X77,X78)
| ~ element(X77,powerset(X78)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
fof(c_0_22,plain,
! [X45] :
( ( empty(X45)
| ~ empty(esk9_1(X45)) )
& ( empty(X45)
| element(esk9_1(X45),powerset(X45)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])])]) ).
fof(c_0_23,plain,
! [X1] : ~ empty(singleton(X1)),
inference(fof_simplification,[status(thm)],[fc2_subset_1]) ).
fof(c_0_24,plain,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[t56_zfmisc_1]) ).
fof(c_0_25,plain,
! [X87] :
( X87 = empty_set
| ~ empty(X87) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])]) ).
fof(c_0_26,plain,
! [X50] :
( empty(esk13_1(X50))
& element(esk13_1(X50),powerset(X50)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(c_0_27,plain,
! [X75,X76] :
( ( subset(X75,singleton(X76))
| X75 != singleton(X76) )
& ( subset(X75,singleton(X76))
| X75 != empty_set )
& ( X75 = singleton(X76)
| X75 = empty_set
| ~ subset(X75,singleton(X76)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t39_zfmisc_1])])])]) ).
cnf(c_0_28,plain,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
( empty(X1)
| element(esk9_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_30,plain,
! [X38] : ~ empty(singleton(X38)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_23])]) ).
fof(c_0_31,negated_conjecture,
~ ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( one_to_one(X1)
<=> ! [X2] :
? [X3] : subset(relation_inverse_image(X1,singleton(X2)),singleton(X3)) ) ),
inference(assume_negation,[status(cth)],[t159_funct_1]) ).
fof(c_0_32,plain,
! [X56,X57] :
( disjoint(X57,X56)
| ~ disjoint(X56,X57) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])])]) ).
fof(c_0_33,plain,
! [X82,X83] :
( disjoint(singleton(X82),X83)
| in(X82,X83) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])]) ).
fof(c_0_34,plain,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ! [X2] :
~ ( ! [X3] : relation_inverse_image(X1,singleton(X2)) != singleton(X3)
& in(X2,relation_rng(X1)) )
<=> one_to_one(X1) ) ),
inference(fof_simplification,[status(thm)],[t144_funct_1]) ).
cnf(c_0_35,plain,
( ~ empty(X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,plain,
empty(esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,plain,
( ~ subset(X1,singleton(X2))
| X1 = singleton(X2)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,plain,
( empty(X1)
| subset(esk9_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_39,plain,
~ empty(singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_40,negated_conjecture,
! [X65,X66] :
( ( subset(relation_inverse_image(esk19_0,singleton(X66)),singleton(esk21_1(X66)))
| one_to_one(esk19_0) )
& ( ~ subset(relation_inverse_image(esk19_0,singleton(esk20_0)),singleton(X65))
| ~ one_to_one(esk19_0) )
& function(esk19_0)
& relation(esk19_0) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])])]) ).
fof(c_0_41,plain,
! [X68,X69] :
( ( ~ relation(X69)
| relation_inverse_image(X69,X68) = empty_set
| ~ disjoint(relation_rng(X69),X68) )
& ( ~ relation(X69)
| disjoint(relation_rng(X69),X68)
| relation_inverse_image(X69,X68) != empty_set ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t173_relat_1])])])]) ).
cnf(c_0_42,plain,
( ~ disjoint(X1,X2)
| disjoint(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_43,plain,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_44,plain,
! [X58,X60,X61] :
( ( ~ function(X58)
| ~ relation(X58)
| relation_inverse_image(X58,singleton(X61)) = singleton(esk18_2(X58,X61))
| ~ in(X61,relation_rng(X58))
| ~ one_to_one(X58) )
& ( ~ function(X58)
| ~ relation(X58)
| one_to_one(X58)
| relation_inverse_image(X58,singleton(esk17_1(X58))) != singleton(X60) )
& ( ~ function(X58)
| ~ relation(X58)
| one_to_one(X58)
| in(esk17_1(X58),relation_rng(X58)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])])])]) ).
fof(c_0_45,plain,
! [X84,X85,X86] :
( ~ empty(X86)
| ~ element(X85,powerset(X86))
| ~ in(X84,X85) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])])]) ).
cnf(c_0_46,plain,
element(esk13_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_47,plain,
esk13_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_48,plain,
( esk9_1(singleton(X1)) = empty_set
| esk9_1(singleton(X1)) = singleton(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_49,negated_conjecture,
( subset(relation_inverse_image(esk19_0,singleton(X1)),singleton(esk21_1(X1)))
| one_to_one(esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,plain,
( ~ relation(X1)
| ~ disjoint(relation_rng(X1),X2)
| relation_inverse_image(X1,X2) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_51,plain,
( in(X2,X1)
| disjoint(X1,singleton(X2)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_52,negated_conjecture,
( ~ subset(relation_inverse_image(esk19_0,singleton(esk20_0)),singleton(X1))
| ~ one_to_one(esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_53,plain,
( ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ one_to_one(X1)
| relation_inverse_image(X1,singleton(X2)) = singleton(esk18_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_54,plain,
! [X55] : subset(X55,X55),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_55,plain,
( ~ empty(X3)
| ~ element(X2,powerset(X3))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_56,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
fof(c_0_57,plain,
! [X18,X19,X20,X21,X22,X23] :
( ( X23 = singleton(X22)
| esk2_2(X22,X23) = X22
| in(esk2_2(X22,X23),X23) )
& ( X23 = singleton(X22)
| esk2_2(X22,X23) != X22
| ~ in(esk2_2(X22,X23),X23) )
& ( X19 != singleton(X18)
| in(X21,X19)
| X21 != X18 )
& ( X19 != singleton(X18)
| X20 = X18
| ~ in(X20,X19) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tarski])])])])])])]) ).
cnf(c_0_58,plain,
( ~ empty(esk9_1(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_59,plain,
( singleton(X1) != empty_set
| esk9_1(singleton(X1)) = empty_set ),
inference(ef,[status(thm)],[c_0_48]) ).
cnf(c_0_60,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
fof(c_0_61,plain,
! [X10,X11,X12,X13,X14,X15,X16] :
( ( ~ function(X10)
| ~ relation(X10)
| X16 = relation_inverse_image(X10,X15)
| in(esk1_3(X10,X15,X16),X16)
| in(apply(X10,esk1_3(X10,X15,X16)),X15) )
& ( ~ function(X10)
| ~ relation(X10)
| X16 = relation_inverse_image(X10,X15)
| in(esk1_3(X10,X15,X16),X16)
| in(esk1_3(X10,X15,X16),relation_dom(X10)) )
& ( ~ function(X10)
| ~ relation(X10)
| X16 = relation_inverse_image(X10,X15)
| ~ in(apply(X10,esk1_3(X10,X15,X16)),X15)
| ~ in(esk1_3(X10,X15,X16),relation_dom(X10))
| ~ in(esk1_3(X10,X15,X16),X16) )
& ( ~ function(X10)
| ~ relation(X10)
| X12 != relation_inverse_image(X10,X11)
| in(X14,X12)
| ~ in(apply(X10,X14),X11)
| ~ in(X14,relation_dom(X10)) )
& ( ~ function(X10)
| ~ relation(X10)
| X12 != relation_inverse_image(X10,X11)
| ~ in(X13,X12)
| in(apply(X10,X13),X11) )
& ( ~ function(X10)
| ~ relation(X10)
| X12 != relation_inverse_image(X10,X11)
| ~ in(X13,X12)
| in(X13,relation_dom(X10)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d13_funct_1])])])])])])]) ).
fof(c_0_62,plain,
! [X25,X26,X27,X29,X30,X31,X33] :
( ( ~ function(X25)
| ~ relation(X25)
| X31 = relation_rng(X25)
| in(esk4_2(X25,X31),X31)
| esk4_2(X25,X31) = apply(X25,esk5_2(X25,X31)) )
& ( ~ function(X25)
| ~ relation(X25)
| X31 = relation_rng(X25)
| in(esk4_2(X25,X31),X31)
| in(esk5_2(X25,X31),relation_dom(X25)) )
& ( ~ function(X25)
| ~ relation(X25)
| X31 = relation_rng(X25)
| esk4_2(X25,X31) != apply(X25,X33)
| ~ in(X33,relation_dom(X25))
| ~ in(esk4_2(X25,X31),X31) )
& ( ~ function(X25)
| ~ relation(X25)
| X26 != relation_rng(X25)
| in(X29,X26)
| X29 != apply(X25,X30)
| ~ in(X30,relation_dom(X25)) )
& ( ~ function(X25)
| ~ relation(X25)
| X26 != relation_rng(X25)
| ~ in(X27,X26)
| X27 = apply(X25,esk3_3(X25,X26,X27)) )
& ( ~ function(X25)
| ~ relation(X25)
| X26 != relation_rng(X25)
| ~ in(X27,X26)
| in(esk3_3(X25,X26,X27),relation_dom(X25)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_funct_1])])])])])])]) ).
cnf(c_0_63,plain,
( ~ function(X1)
| ~ relation(X1)
| relation_inverse_image(X1,singleton(esk17_1(X1))) != singleton(X2)
| one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_64,negated_conjecture,
( one_to_one(esk19_0)
| relation_inverse_image(esk19_0,singleton(X1)) = empty_set
| singleton(esk21_1(X1)) = relation_inverse_image(esk19_0,singleton(X1)) ),
inference(spm,[status(thm)],[c_0_37,c_0_49]) ).
cnf(c_0_65,plain,
( ~ relation(X1)
| in(X2,relation_rng(X1))
| relation_inverse_image(X1,singleton(X2)) = empty_set ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_66,negated_conjecture,
relation(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_67,plain,
! [X74] : subset(empty_set,X74),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
cnf(c_0_68,negated_conjecture,
( ~ in(X2,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ one_to_one(esk19_0)
| ~ subset(relation_inverse_image(esk19_0,singleton(esk20_0)),relation_inverse_image(X1,singleton(X2))) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_69,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_70,negated_conjecture,
function(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_71,plain,
( ~ in(X2,empty_set)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_72,plain,
( X2 = singleton(X1)
| esk2_2(X1,X2) = X1
| in(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_73,plain,
singleton(X1) != empty_set,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60])]),c_0_39]) ).
cnf(c_0_74,plain,
( ~ function(X2)
| ~ relation(X2)
| X4 != relation_inverse_image(X2,X3)
| ~ in(apply(X2,X1),X3)
| ~ in(X1,relation_dom(X2))
| in(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_75,plain,
( ~ function(X2)
| ~ relation(X2)
| X3 != relation_rng(X2)
| ~ in(X1,X3)
| X1 = apply(X2,esk3_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_76,plain,
( ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2)
| in(esk3_3(X1,X2,X3),relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_77,negated_conjecture,
( ~ function(X2)
| ~ relation(X2)
| relation_inverse_image(X2,singleton(esk17_1(X2))) != relation_inverse_image(esk19_0,singleton(X1))
| one_to_one(X2)
| one_to_one(esk19_0)
| relation_inverse_image(esk19_0,singleton(X1)) = empty_set ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_78,negated_conjecture,
( in(X1,relation_rng(esk19_0))
| relation_inverse_image(esk19_0,singleton(X1)) = empty_set ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_79,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_80,negated_conjecture,
( ~ in(esk20_0,relation_rng(esk19_0))
| ~ one_to_one(esk19_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_66]),c_0_70])]) ).
cnf(c_0_81,plain,
( ~ empty(X2)
| esk2_2(X1,empty_set) = X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
fof(c_0_82,plain,
! [X72,X73] :
( in(X72,X73)
| empty(X73)
| ~ element(X72,X73) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
fof(c_0_83,plain,
! [X35] : element(esk6_1(X35),X35),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_84,plain,
( ~ in(X1,relation_dom(X2))
| ~ in(apply(X2,X1),X3)
| ~ function(X2)
| ~ relation(X2)
| in(X1,relation_inverse_image(X2,X3)) ),
inference(er,[status(thm)],[c_0_74]) ).
cnf(c_0_85,plain,
( ~ in(X2,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| apply(X1,esk3_3(X1,relation_rng(X1),X2)) = X2 ),
inference(er,[status(thm)],[c_0_75]) ).
cnf(c_0_86,plain,
( ~ in(X2,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| in(esk3_3(X1,relation_rng(X1),X2),relation_dom(X1)) ),
inference(er,[status(thm)],[c_0_76]) ).
cnf(c_0_87,negated_conjecture,
( one_to_one(esk19_0)
| relation_inverse_image(esk19_0,singleton(esk17_1(esk19_0))) = empty_set ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_77]),c_0_66]),c_0_70])]) ).
cnf(c_0_88,negated_conjecture,
~ one_to_one(esk19_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_78]),c_0_79])]),c_0_80]) ).
cnf(c_0_89,plain,
( esk2_2(X1,X2) != X1
| ~ in(esk2_2(X1,X2),X2)
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_90,plain,
esk2_2(X1,empty_set) = X1,
inference(spm,[status(thm)],[c_0_81,c_0_60]) ).
cnf(c_0_91,plain,
( X2 != singleton(X3)
| ~ in(X1,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_92,plain,
( ~ element(X1,X2)
| in(X1,X2)
| empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_93,plain,
element(esk6_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_94,plain,
( ~ function(X1)
| ~ relation(X1)
| one_to_one(X1)
| in(esk17_1(X1),relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_95,plain,
( ~ in(X2,X3)
| ~ in(X2,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| in(esk3_3(X1,relation_rng(X1),X2),relation_inverse_image(X1,X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]) ).
cnf(c_0_96,negated_conjecture,
relation_inverse_image(esk19_0,singleton(esk17_1(esk19_0))) = empty_set,
inference(sr,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_97,plain,
~ in(X1,empty_set),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_73]) ).
cnf(c_0_98,plain,
( ~ in(X1,singleton(X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_91]) ).
cnf(c_0_99,plain,
( in(esk6_1(X1),X1)
| empty(X1) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_100,negated_conjecture,
( in(esk17_1(esk19_0),relation_rng(esk19_0))
| one_to_one(esk19_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_66]),c_0_70])]) ).
cnf(c_0_101,negated_conjecture,
( ~ in(X1,relation_rng(esk19_0))
| ~ in(X1,singleton(esk17_1(esk19_0))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_66]),c_0_70])]),c_0_97]) ).
cnf(c_0_102,plain,
esk6_1(singleton(X1)) = X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_39]) ).
cnf(c_0_103,negated_conjecture,
in(esk17_1(esk19_0),relation_rng(esk19_0)),
inference(sr,[status(thm)],[c_0_100,c_0_88]) ).
cnf(c_0_104,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_99]),c_0_102]),c_0_103])]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU078+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n005.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 05:49:49 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.50 Running first-order theorem proving
% 0.17/0.50 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.62/0.65 % Version: 3.5.1
% 0.62/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.62/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.62/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.62/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.62/0.65 % Starting new_bool_1 with 300s (1) cores
% 0.62/0.65 % Starting sh5l with 300s (1) cores
% 0.62/0.65 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2688674 completed with status 0
% 0.62/0.65 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.62/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.62/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.62/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.62/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.62/0.65 % No SInE strategy applied
% 0.62/0.65 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.62/0.65 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 0.62/0.65 % Starting SubtermCWHack with 136s (1) cores
% 0.62/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.62/0.65 % Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I with 113s (1) cores
% 0.62/0.65 % Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SE_S0Y with 113s (1) cores
% 0.62/0.65 % Starting G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with 113s (1) cores
% 0.62/0.65 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2688679 completed with status 0
% 0.62/0.65 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.62/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.62/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.62/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.62/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.62/0.65 % No SInE strategy applied
% 0.62/0.65 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.62/0.65 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 0.62/0.65 % Starting SubtermCWHack with 136s (1) cores
% 0.62/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.62/0.65 % Preprocessing time : 0.003 s
% 0.62/0.65 % Presaturation interreduction done
% 0.62/0.65
% 0.62/0.65 % Proof found!
% 0.62/0.65 % SZS status Theorem
% 0.62/0.65 % SZS output start CNFRefutation
% See solution above
% 0.62/0.65 % Parsed axioms : 43
% 0.62/0.65 % Removed by relevancy pruning/SinE : 0
% 0.62/0.65 % Initial clauses : 82
% 0.62/0.65 % Removed in clause preprocessing : 2
% 0.62/0.65 % Initial clauses in saturation : 80
% 0.62/0.65 % Processed clauses : 717
% 0.62/0.65 % ...of these trivial : 9
% 0.62/0.65 % ...subsumed : 336
% 0.62/0.65 % ...remaining for further processing : 372
% 0.62/0.65 % Other redundant clauses eliminated : 15
% 0.62/0.65 % Clauses deleted for lack of memory : 0
% 0.62/0.65 % Backward-subsumed : 23
% 0.62/0.65 % Backward-rewritten : 14
% 0.62/0.65 % Generated clauses : 1674
% 0.62/0.65 % ...of the previous two non-redundant : 1408
% 0.62/0.65 % ...aggressively subsumed : 0
% 0.62/0.65 % Contextual simplify-reflections : 17
% 0.62/0.65 % Paramodulations : 1644
% 0.62/0.65 % Factorizations : 4
% 0.62/0.65 % NegExts : 0
% 0.62/0.65 % Equation resolutions : 17
% 0.62/0.65 % Disequality decompositions : 0
% 0.62/0.65 % Total rewrite steps : 774
% 0.62/0.65 % ...of those cached : 727
% 0.62/0.65 % Propositional unsat checks : 0
% 0.62/0.65 % Propositional check models : 0
% 0.62/0.65 % Propositional check unsatisfiable : 0
% 0.62/0.65 % Propositional clauses : 0
% 0.62/0.65 % Propositional clauses after purity: 0
% 0.62/0.65 % Propositional unsat core size : 0
% 0.62/0.65 % Propositional preprocessing time : 0.000
% 0.62/0.65 % Propositional encoding time : 0.000
% 0.62/0.65 % Propositional solver time : 0.000
% 0.62/0.65 % Success case prop preproc time : 0.000
% 0.62/0.65 % Success case prop encoding time : 0.000
% 0.62/0.65 % Success case prop solver time : 0.000
% 0.62/0.65 % Current number of processed clauses : 239
% 0.62/0.65 % Positive orientable unit clauses : 39
% 0.62/0.65 % Positive unorientable unit clauses: 0
% 0.62/0.65 % Negative unit clauses : 16
% 0.62/0.65 % Non-unit-clauses : 184
% 0.62/0.65 % Current number of unprocessed clauses: 805
% 0.62/0.65 % ...number of literals in the above : 3861
% 0.62/0.65 % Current number of archived formulas : 0
% 0.62/0.65 % Current number of archived clauses : 123
% 0.62/0.65 % Clause-clause subsumption calls (NU) : 9185
% 0.62/0.65 % Rec. Clause-clause subsumption calls : 4184
% 0.62/0.65 % Non-unit clause-clause subsumptions : 183
% 0.62/0.65 % Unit Clause-clause subsumption calls : 395
% 0.62/0.65 % Rewrite failures with RHS unbound : 0
% 0.62/0.65 % BW rewrite match attempts : 17
% 0.62/0.65 % BW rewrite match successes : 11
% 0.62/0.65 % Condensation attempts : 0
% 0.62/0.65 % Condensation successes : 0
% 0.62/0.65 % Termbank termtop insertions : 31565
% 0.62/0.65 % Search garbage collected termcells : 1060
% 0.62/0.65
% 0.62/0.65 % -------------------------------------------------
% 0.62/0.65 % User time : 0.087 s
% 0.62/0.65 % System time : 0.010 s
% 0.62/0.65 % Total time : 0.097 s
% 0.62/0.65 % Maximum resident set size: 3668 pages
% 0.62/0.65
% 0.62/0.65 % -------------------------------------------------
% 0.62/0.65 % User time : 0.341 s
% 0.62/0.65 % System time : 0.041 s
% 0.62/0.65 % Total time : 0.382 s
% 0.62/0.65 % Maximum resident set size: 4864 pages
% 0.62/0.65 % E exiting
%------------------------------------------------------------------------------